Ideal band insulation and transitionless quantum driving

Subjecting band insulators to electric fields generally induces transitions between the (filled) valence bands and the (empty) conduction bands. By applying ideas related to Berry's notion of transitionless quantum driving, we search for auxiliary fields capable of mitigating these transitions, so as to foster ideal insulating characteristics, even in the presence of time-dependent uniform electric fields. So far, transitionless quantum driving has primarily been invoked to suppress transitions state by state. However, the many-fermion character of the present setting of band insulators renders less stringent the challenge of engineering suitable auxiliary fields. Specifically, because the valence band is filled, and by identical particles, one need only mitigate transitions band by band. As a result, there is a broader family of auxiliary fields to choose from. This feature creates the opportunity for optimizing within a class of experimentally feasible (if not perfect) auxiliary fields, and thus of bringing systems close to ideal band insulation.